Finding Constant and Average Rates

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  • 0:05 What Is a Constant Rate?
  • 0:30 What Is an Average Rate?
  • 1:23 Finding a Constant Rate
  • 3:29 Finding an Average Rate
  • 5:53 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson to learn the differences between constant and average rates. You will learn the steps you need to take to find them and get two great visuals you can keep in mind to help you solve these rate problems.

What Is a Constant Rate?

So, what exactly is a constant rate? Well, a constant rate is something that changes steadily over time. Picture the burning of a candle. That is a constant rate because a candle burns down steadily over time. We can be confident that if a particular candle takes so many hours to burn down, and we make the candle twice as big, we will have a candle that will burn twice as long.

What Is an Average Rate?

Now, what about the average rate? An average rate is different from a constant rate in that an average rate can change over time. An average rate is actually the average or overall rate of an object that goes at different speeds or rates over a period of time. For this one, picture the flight of a bumblebee.

The bumblebee sees a flower and rushes over to the flower at a quick speed. Once it's there, the bumblebee slows down and slowly buzzes around the flower to inspect it. Oh, but look! There's another even bigger flower in the distance. The bumblebee sees it and buzzes off at an even quicker speed.

The average rate of the bumblebee would take all these different speeds and find the average speed the bumblebee had over his whole trip.

Now that we've covered these definitions, let's see how we can find each of these rates. We will stick to our original visuals to help us out with our problems.

Finding a Constant Rate

Let's go back to our burning candle to help us with finding a constant rate.

We are taking a test, and we see this problem in front of us: Object A takes 1 hour to burn 1 inch, and Object B takes 2 hours to burn down 1 inch. What is the constant rate of each object?

Okay, another dry math problem. But, that's okay! We have our useful visual we can refer to, so we won't be bored. We can picture two differently sized candles. We can get creative here and make the problem more fun. We can have one rainbow colored candle and another candle with a lightning bolt drawing on the side. Picture anything that keeps your interest.

Now that we have our candles in front of us, we can get to the meat of the problem and find the constant rates of each candle.

We will call the rainbow colored candle Object A, and we will call the lightning bolt candle Object B. I'm picturing my rainbow colored candle burning. I see that for each hour that passes, my rainbow colored candle goes down by an inch. To calculate my constant rate for this candle, this object, I recall the formula for rate, which is rate = distance / time.

Okay. So, I don't have a distance, per se. But I do have the amount of candle burned, which is 1 inch. I also have a time, which is 1 hour. I plug these numbers into my formula to get my constant rate. I get 1 / 1, which gives me 1. So, my constant rate for my rainbow colored candle, or Object A, is 1 inch per hour. That is part of my answer.

The other part of my answer is the rate for the lightning bolt candle, or Object B. I will do the same and plug in 1 for the amount of candle burned, or the distance, and 2 hours for my time. My constant rate here, then, is 1 / 2. or 0.5 inches per hour.

Now I'm done with this problem. Object A takes 1 hour to burn 1 inch, and Object B takes 2 hours to burn down 1 inch. What is the constant rate of each object? I have found that my answer for this problem is 1 inch per hour for Object A and 0.5 inches per hour for Object B.

Finding an Average Rate

To help us out with an average rate problem, let's go back to our bumblebee visual.

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